Nanostructured dielectric materials for high energy density multi layer ceramic capacitors

ABSTRACT

A high energy density multilayer ceramic capacitor, having at least two electrode layers and at least one substantially dense polycrystalline dielectric layer positioned therebetween. The at polycrystalline dielectric layer has an average grain size of less than about 300 nanometers, a particle size distribution of between about 150 nanometers and about 3 micrometers, and a maximum porosity of about 1 percent. The dielectric layer is selected from the group including TiO 2 , BaTiO 3 , Al 2 O 3 , ZrO 2 , lead zirconium titanate, and combinations thereof and has a breakdown strength of at least about 1100 kV per centimeter.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of co-pending U.S. patent applicationSer. No. 12/580,373, filed on Aug. 29, 2009, and claims prioritythereto.

GRANT STATEMENT

The invention was made in part from government support under Grant No.RG001083 from the National Science Foundation (NSF/IUCRC Center forDielectric Studies) and under Grant No. N000-14-05-1-0541 from theOffice of Naval Research. The U.S. Government has certain rights in theinvention.

TECHNICAL FIELD

The present invention relates to the field of ceramic science and, moreparticularly high energy density multilayer ceramic capacitors.

BACKGROUND

Titanium dioxide (TiO₂) is one of the most widely used ceramicmaterials, having a broad range of applications such as pigments,sensors, waste treatment, solar cells and capacitors. NanocrystallineTiO₂ ceramics have been the subject of great interest to researchersover the years. Research has been conducted in such diverse areas asTiO₂ nanopowder synthesis, thin film fabrication, and the sintering ofbulk ceramics. However, thus far pure TiO₂ nanopowder material hasseldom been used as a dielectric material for capacitor applications asit can easily be reduced, leading to devices having lower resistivityand high dielectric loss, even though the intrinsic dielectric loss ofstoichiometric TiO₂ is very low.

Therefore, there is a need to provide a new and improved bulk TiO₂material characterized by nano-scale grain size that might contribute tothe achievement of the desired overall dielectric properties forapplications in high energy density capacitors. There is also acorresponding need to provide a new and improved method for fabricatinga TiO₂ material having a nano-scale grain size. The present inventionaddresses these needs.

SUMMARY OF INVENTION

In one aspect of the invention, a new and improved ceramic material forhigh energy density capacitor applications is described. The inventiveceramic material comprises at least one layer of dense dielectricceramic with nano-size grain and substantially no residual porosity. Theexemplary dielectric ceramic materials are TiO₂, alumina, stabilizedZrO₂, BaTiO₃, and PZT.

In another aspect of the invention, a method for producing substantiallytheoretically dense nano-structured dielectric ceramic material isdescribed. The fabrication method includes the steps of 1) compacting apreselected ceramic powder into a green body, and 2) sintering the greenbody in an oxidizing atmosphere, such as substantially pure oxygen, at apre-selected time/temperature profile. For example, the sinteringtemperature for TiO₂ may range from 750° C. to 1200° C., with less than900° C. being typical, while the soak time at 750° C. may be about 13hours while the soak time at 1200° C. may be around 2-3 hours.

In yet another aspect of the invention, a new and improved high energydensity capacitor is described. The high energy density capacitorincludes at least one layer of substantially dense TiO₂ ceramic materialwith a substantially nano-sized grain structure. As used herein, highenergy density generally means greater than about 2 J/cm³, and nanoscalegenerally means particles smaller than about 500 nanometers in diameteror major axial direction. Such dielectric materials may be used tofabricate Multi Layer Ceramic Capacitors (MLCCs).

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic illustration of a multilayer capacitor accordingto a first embodiment of the present invention.

FIG. 2 summarizes the sintering profiles of sintered titania bodieshaving microstructures characterized by nano-scale grain size andparticle size distributions according to a second embodiment of thepresent invention.

FIG. 3 is a schematic illustration of a body of FIG. 2 having a dimpledelectrode configuration for BDS measurement.

FIG. 4 is the SEM photomicrograph of precursor TiO₂ nano powders.

FIG. 5 is a plot illustrating the XRD profiles of precursor powder andtwo sintered bodies (T1200A and T750).

FIG. 6A is a first SEM photomicrograph of the sintered bodies.

FIG. 6B is a second SEM photomicrograph of the sintered bodies.

FIG. 6C is a third SEM photomicrograph of the sintered bodies.

FIG. 6D is a fourth SEM photomicrograph of the sintered bodies.

FIG. 7A is a plot illustrating the dielectric constants of the sinteredbodies.

FIG. 7B is a plot illustrating the dielectric loss of the sinteredbodies.

FIG. 8 is a plot illustrating the polarization vs. electrical field ofthe sintered bodies.

FIG. 9 is a plot illustrating the current-voltage characteristics ofTiO2 ceramics sintered in various conditions.

FIG. 10 is an Arrhenius plot of conductivity of TiO₂ ceramics sinteredin various conditions.

FIG. 11A shows complex impedance spectra of TiO₂ ceramics sintered invarious conditions.

FIG. 11B shows the fitted curves of sample T9001C and T1200A.

FIG. 12 is a plot showing the imaginary parts of impedance (Z″) versusfrequency.

FIG. 13 is a plot illustrating dielectric breakdown strength of TiO₂ceramics sintered in various conditions.

FIG. 14 is a plot illustrating the I-V curve during the breakdownstrength test.

DETAILED DESCRIPTION OF INVENTION

For the purposes of promoting an understanding of the principles of thenovel technology, reference will now be made to the embodimentsillustrated in the drawings and specific language will be used todescribe the same. It will nevertheless be understood that no limitationof the scope of the novel technology is thereby intended, suchalterations and further modifications in the illustrated device, andsuch further applications of the principles of the novel technology asillustrated therein being contemplated as would normally occur to oneskilled in the art to which the novel technology relates.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. All publications, patentapplications, patents, and other references mentioned herein areincorporated by reference in their entirety.

The properties of ceramics (both mechanical properties and electricalproperties) heavily depend on their microstructural features, such asgrain size, porosity, secondary phase and the like, and it is possibleto enhance some desired properties by manipulating the microstructure ofceramics. The invention defines a new and improved nanostructuredceramic material with attractive dielectric properties, such as lowintrinsic dielectric loss and high breakdown strength.

Generally there are two key parameters that will determine the energydensity of dielectric materials: one is the dielectric constant and theother is dielectric breakdown strength (highest field the dielectricmaterial can withstand). The volumetric energy density of dielectrics isdetermined by:

$\begin{matrix}{w = {\int_{0}^{Eb}{ɛ_{0}{ɛ_{r}(E)}E\ {E}}}} & (1)\end{matrix}$

where W is volumetric energy density (J/cm³), ∈₀ is the permittivity offree space, ∈_(r) is the relative permittivity of the dielectricmaterial, E is the electrical field, and E_(b) is the dielectricbreakdown strength. For linear dielectric materials, equation (1) can besimplified to

W=½∈₀∈_(r) E _(b) ²  (2)

which implies that the energy density is primarily a function of thedielectric breakdown strength.

According to a first embodiment, the novel nanostructured dielectricmaterial is composed of at least one layer of nanostructured dielectricceramic material. In other words, the ceramic material has a nano-scalegrain size and no residual porosity. One exemplary material is titania(TiO₂). As grain size decreases from 10 μm to 200 nm, the breakdownstrength of TiO₂ increases from about 550 KV/cm to about 1100 KV/cm.Referring to Eq. 2, nanostructured and dense TiO₂ having increasedbreakdown strength should be a good candidate material for high energydensity capacitors. Other nanostructured and dense dielectrics materialsincluding but not limited to Al₂O₃, stabilized ZrO₂, BaTiO₃, and PZTshould also exhibit high electrical breakdown strength as compared totheir conventional counterparts having a grain structure in micrometerrange (>1 μm). Typical grain size and density limits for nanostructureddielectrics are less than about 300 nm and greater than about 99.9% oftheoretical density (or less than about 0.1% porosity), respectively.

The present invention also provides a method for fabrication of thenovel dielectric material, which typically includes at least one layerof nanostructured dielectric ceramic material. The inventive fabricationmethod generally comprises the steps of 1) compacting a pre-selecteddielectric material powder into a pellet and 2) sintering the pellet ina substantially oxidizing atmosphere, such as pure oxygen, and at apredetermined temperature and for a predetermined length of time, suchthat the time/temperature profile is sufficient to sinter the dielectricmaterial to substantially theoretical density without giving rise toundue grain growth and yielding a microstructure characterized bysubstantially uniform grain size.

The invention provides an exemplary fabrication of nanostructured TiO₂.Specifically, any commercially available nanosized TiO₂ powders(particle size <50 nm) may be selected as starting material for theinventive nanostructured TiO₂. In the compacting step, the powders maybe compressed by any convenient method, such as uniaxially compacted ina die at about 50 MPa to obtain a pellet, may then be staticallycompacted at a pressure of about 300 MP; however, any convenientcompaction method may be used to produce a green body pellet orsubstrate.

In the sintering step, the densification of the green body may beconducted at sufficient temperature, typically between about 750°C.-1200° C., in a sufficiently oxidizing atmosphere, such as pure oxygenat ambient pressure or flowing air, and with a sufficiently slow coolingprofile (such as furnace cooling or a cooling rate of about 1° C./min orless). Sintering in an oxidizing atmosphere and cooling at slow rates(less than about 1° C./min) facilitate oxidation (or at least retardreduction) of the oxide dielectric material (in this example, TiO₂),which results in more uniform and thus improved dielectric properties ofthe material. During the oxygenation process, the number of oxygenvacancies in TiO₂ is reduced to yield a material having reduced loss andleakage current.

Another aspect of the present novel technology is the provision of a newand improved high energy density capacitor that incorporates at least alayer of nanostructured ceramic material as described herein, andtypically with a multilayered structure. For example, the multiplelayers of the nanostructured TiO₂ separated by layers of electrodematerial may be employed to build single or multilayer ceramiccapacitors for applications requiring high energy density storage (>5J/cm³). A schematic drawing of a multilayer capacitor 10 is shown FIG.1, with the nanostructured TiO₂ layer 15 and the electrode layer 20staged in alternative to each other. Alternate electrode layers 20 areelectrically connected to each terminal end or termination 25,respectively. MLCCs are essentially stacks of capacitors packagedtogether, and take advantage of the phenomena that energy storageincreases as the number and area of the dielectric layers increase andthe thicknesses of the dielectric layers decrease.

EXAMPLES I Microstructural Developments and General Testing Conditions

NANOTEK® TiO₂ powders were obtained as starting materials for MLCCproduction, with powder characteristics and main impurity levelsreproduced from the included product data sheet as Tables 1 and 2,respectively (NANOTEK is a registered trademark of NanophaseTechnologies Corporation, 1319 Marquette Drive, Romeoville, Ill., 60446,Reg. No. 1978354). Green compacts were prepared by uniaxial pressing at50 MPa and subsequent cold isostatic pressing at 300 MPa. Sintering wasconducted at various temperatures (750° C.-1200° C.) in pure oxygen (1atm.) or air with different cooling rates (furnace cooling or 1° C./mincooling rate).

TABLE 1 Characteristics of the starting powders Characteristics ValuePurity 99.9% Average particle size (nm) 40 Specific surface area (m²/g)38 Bulk density (g/cm³) 0.20 True density (g/cm³) 3.95 Crystal phase 80%anatase and 20% rutile

TABLE 2 Main impurities in the TiO₂ powder Elements Impurity level (%)Fe 0.037 Mg 0.032 gCa 0.024 Al 0.0089

FIG. 2 summarizes the sintering profiles of each sample, among whichprofile 1 was conducted according to a two-step sintering procedure. Thetwo-step sintering process involves a rapid heating of a green body to apredetermined temperature, typically without a hold-time, followed by arapid cooling to a lower temperature at which the presintered materialis soaked for a relatively long time in order to achieve densification.While this two-step technique has been effective in some cases to obtaindense ceramics with very small grain size or little grain growth duringsintering, the two-step process is typically unnecessary to achievedensified nanostructured titania and like substrates. Conventionalsintering, at heating rates on the order of 5° C./min up to about 800°C. and with 6 hours soak time in oxygen or oxidizing atmospheres wassufficient to achieve substrates having excellent dielectric properties.

The relative density of each sample was determined by Archimedes' methodusing water as the immersion liquid and assuming the theoretical densityof anatase and rutile TiO₂ are 3.89 g/cm³ and 4.25 g/cm³, respectively.Phase evolution was identified by XRD and the microstructure of theas-fired surface of TiO₂ ceramics was observed by SEM. Grain size wasdetermined by the liner intercept method on SEM photomicrographs.

Samples of 10 mm diameter and 0.6 mm thickness were prepared forelectrical property measurements. The sample surfaces were polished via1 μm diamond suspension and painted with sliver paste as top and bottomelectrodes. After electroding, the samples were baked at 300° C. toensure good contact between sample surface and the silver electrodes.D.C. conductivity and current-voltage characteristics were measured by atwo-probe method in ambient atmosphere. Impedance spectroscopy wasmeasured in the frequency range of 1 Hz-1 MHz with a voltage amplitudeof 1V and analyzed. Relative dielectric constant values were calculatedfrom the capacitance as measured. Polarization versus electrical fieldrelationships were measured on a ferroelectric tester. For breakdownstrength (BDS) measurements, D.C. voltage was supplied by a high voltagegenerator with a fixed ramp rate of 200V/second.

A dimpled electrode configuration was employed for BDS measurements, asshown in FIG. 3, so as to minimize contributions of edge-effects of theelectric field and thus enjoy the maximum electrical stressconcentration at the bottom of the dimple, as this specific specimenconfiguration reduces/suppresses the phenomenon of edge breakdown.

II Sample Characterization

FIG. 4 is the SEM image of the starting powders, which shows that thepowders are typically composed of particles that are generally sphericalin shape and with a particle size less than 50 nm. The relative densityof TiO₂ ceramics sintered in various conditions is summarized in Table3. Table 3 shows that except for sample T750, all the other samplesachieved a relative density higher than 98%. By using the two-stepsintering procedure, nanosized TiO₂ powders can be sintered to arelative density of about 96% at temperatures as low as 750° C. Allsamples sintered at 900° C. achieved almost identical relative densitiesof about 99%, suggesting that sintering atmosphere and cooling rate donot have a significant effect on the densification process.

TABLE 3 Relative density obtained in various sintering conditions SampleRelative Sintering conditions name density (%)  850° C.-750° C. 12 h inO₂ T750 95.61 1° C./min cooling rate  900° C. 2 h in air furnace coolingT900A 99.23  900° C. 2 h in O₂ furnace cooling T900F 98.80  900° C. 2 hin O₂ 1° C./min T9001C 98.89 cooling rate 1200° C. 2 h in air furnacecooling T1200A ~100

FIG. 5 shows the XRD patterns of the samples (T750 and T1200A) sinteredin different conditions together with the staring powder (Powder). Asshown in FIG. 5, the starting powder is mainly composed of anatase,while there is no anatase phase left in the sintered samples. Normally,the anatase to rutile transition temperature is about 915° C. In thiscase, nanosized starting powders may help to reduce the transitiontemperature. No secondary phase is detected, therefore, as sinteredsamples are all phase pure rutile TiO₂.

FIGS. 6A to 6D show the representative SEM images of the microstructureof TiO₂ ceramic substrates 50 sintered at different conditions. FIG. 6Ashows that the grain size is about 150 nm for specimen 50 sintered at750° C.; FIG. 6B shows that the grain size is about 300 nm for asubstrate 50 sintered at 900° C.; and FIGS. 6C and 6D show that thegrain sizes further grow to about 3 μm after sintering substrates 50 at1200° C. Furthermore, as shown in FIGS. 6A to 6D, the bimodaldistribution of grain size indicates that grain grows via anOswald-ripping mechanism.

III Dielectric Properties of the Samples

FIG. 7A shows the dielectric constant of each sintered sample. Over thefrequency range from 100 Hz to 100K Hz, the dielectric constants of allsamples show little or no dispersive characteristics. As shown in FIG.7A, sample T750 has the lowest dielectric constant around 125, while theother samples have higher dielectric constants about 145. Residualporosity is believed to be the major reason that leads to lowerdielectric constant of sample T750. The previous studies have shown thatthe dielectric constant of TiO₂ single crystal (rutile) alongc-orientation is about 170 and along the a-orientation is about 86. Therandomly orientated polycrystalline TiO₂ ceramics is believed to have adielectric constant around 100. The sintered samples tend to be slightlyoriented, resulting in the higher dielectric constants than expected.

FIG. 7B illustrates the dielectric loss of the sintered samples.Dielectric loss is generally low, especially in the high frequencyrange, such that the dielectric loss is about 0.04% for sample T9001C at100K Hz. In FIG. 7B, sample T1200A has the highest dielectric lossfollowed by sample T750. The relative high dielectric loss of sampleT750 may be attributed to its surface conduction due to its relativelylow density. Samples T1200A was sintered in air at high temperature,indicating that the loss may associate with oxygen vacancies generatedduring high temperature sintering.

It is widely believed that the predominant defects in n-type TiO₂ areoxygen vacancies, which may be expressed by Kröger-Vink notation asfollows:

O _(o) ^(X) =V _(o) ^()+2e′+½O ₂  (3)

Based on equation (3), two extra electrons may be generated for eachoxygen vacancy created. As a result, relatively high conductivity isexpected in samples with high concentration of oxygen vacancies. Asshown in FIG. 7B, the dielectric loss increases with decreasingfrequency for sample T1200A, which may be a characteristic of conductionloss, since normally conduction loss is the dominate loss mechanism atlower frequencies.

FIG. 8 shows the Polarization versus Electric field (P-E) relationshipof two sintered samples (T9001C and T1200A). As shown in FIG. 8, the P-Ecurve of Sample T1200A demonstrates hysteresis loop, an indication ofconduction loss. On the contrary, the P-E curve of Sample T9001C is of alinear P-E relation with polarization about 1.25 μC/cm² at 62 KV/cm. Acalculation based on the slope of the P-E curve of Sample T9001C gives adielectric constant of 228, which is higher than what measured in FIG.7A. Since polarization was measured at low frequency, enhanceddielectric constant may come from the contribution of space chargepolarization.

FIG. 9 plots the Current-Voltage (I-V) characteristics of the sinteredsamples, where the leakage current densities were measured at 200° C. inambient air. Sample T1200A demonstrated the highest leakage current witha non-linear behavior. The similar behavior has been found in singlecrystal rutile, which indicates field dependent conductivity, especiallyfor reduced samples (Grant, 1959). The non-linear I-V characteristicobserved of Sample T1200A is also an indication that this sample is notelectrically uniform, some part of the microstructure (most likely grainboundaries) may start to breakdown at higher field strength. Thisphenomenon will be discussed in more detail below together with theinterpretation of impedance spectra.

The Current-Voltage characteristics for the other samples are of thelinear or ohmic behavior. As expected, sample T9001C, which was sinteredin oxygen atmosphere and cooled off at a gradual cooling rate (1°C./min), has the lowest leakage current. Once again, a sinteringcondition in oxygen atmosphere followed by slow cooling is believed tohelp minimize the oxygen vacancy concentration and electricalconductivity. Particularly, the cooling rate is of interest as thedefects concentration may ‘freeze’ at the high temperature level ifthere is not enough time for the sample to equilibrate with thesintering atmosphere during the cooling off process.

FIG. 10 is an Arrhenius plot of conductivity of three sintered samplesmeasured at low field (˜160V/cm). Sample T1200A has the highestconductivity especially at high temperature range, while Sample T9001Cdemonstrates the lowest conductivity especially at low temperaturerange.

The conductivity can be used to determine the activation energy (E_(a)),which can be calculated in the temperature range of 200° C.-500° C.according to the following equation:

σ=σ₀ exp(−E _(a) /kT)  (4)

where σ, σ₀, k, and E_(a) represent the conductivity, pre-exponentialfactor, Boltzmann constant and activation energy of mobile chargecarriers, respectively.

The activation energies obtained in this study range from 0.86 eV to1.21 eV, which are typical values of migration enthalpy for ionicdefects. The activation energies of the sintered sample obtained in thisstudy are comparable with literature, while less than those obtainedfrom the single crystal samples. Sample T750's activation energy is muchlower than those of the others, which may indicating a small grain sizesample has lower activation energy. Similar phenomenon has also beenobserved in CeO_(2-x) samples, which suggested that the atomic levelorigin of this behavior lies in the lower vacancy formation enthalpy atgrain boundary sites.

FIG. 10 also shows that the linear relationship between conductivity andreciprocal temperature cannot be extended to temperature lower than 150°C. At 50° C., the conductivities of all three samples (˜10⁻¹² S/cm) aremuch higher than the extrapolated values (would be in the range of 10⁻¹⁶to 10⁻¹⁴ S/cm). The elevation of conductivity at low temperatureindicates that the dominant conduction mechanism is ionic conduction,because at lower temperatures ions will not have enough thermal energyto substantially move. Interestingly, the conductivities measured at 50°C. are actually higher than those measured at 100° C. for sample T9001Cand T750. This behavior may due to the effects of surface conduction inthe presence of moisture.

Impedance spectroscopy is a powerful technique used to characterizeelectronic ceramics, since it allows the intrinsic (bulk) properties tobe distinguished from extrinsic contributions such as grain boundaries,surface layers, and electrode contact variations. The electricalresponses of the sintered samples in the frequency range of 1 Hz to 1MHz were measured at 500° C. and plotted in cole-cole curves as shown inFIG. 11A. In the order of T750-T9001C-T900E-T900A-T1200A, the overallresistances (intercept with the real axis, Z′) of the samples decreasesequentially, which is in agreement with the D.C. conductivitymeasurements. Except for Sample T1200A, which shows two overlapped anddepressed semi-circle, the plots of the cole-cole curves for theremaining samples have the general form of semi-circles.

The impedance spectra can be well fitted by using two R-C(resistor-capacitor) or R-CPE (resistor-constant phase element) parallelcircuit elements connected in series, as shown in FIG. 11B. In FIG. 11B,the larger semi-circular plot is the response of the grain since thedielectric constant calculated based on capacitance value is around 150corresponding well with the previous dielectric constant measurement.The second, smaller semi-circular plot located in the lower frequencyrange is normally attributed to the grain boundary response. Grainboundaries typically have higher electrical resistance (R) andcapacitance (C) as compared to the R and C values of the grainsthemselves, and therefore the grain boundary relaxation time τ=RC iscorrespondingly larger. At characteristic frequency f=(2πτ)⁻¹, the grainboundary frequency is lower than that of the grain.

By plotting the imaginary components of impedance, Z″, againstfrequency, as shown in FIG. 12, the responses of the grain and the grainboundary can be separated more clearly. As Z″ is dominated by the mostresistive element, it can be seen that for samples T750, T900A, T900F,and T9001C, the high frequency grain response dominates the resistivityof the sample, while for sample T1200A, the low frequency grain boundaryresponse dominates the resistivity of the sample.

The observation of a significant grain boundary response in T1200A isinteresting. The total grain boundary resistivites, (R_(T), Ω/m³), ofT9001C and T1200A are very close to theoretical prediction. Since thedifference in mean grain sizes (d, m) of these samples is about oneorder of magnitude, there is a corresponding order of magnitudedifference in specific grain boundary resistivity (R_(S), Ω/m²)according to the following equation:

$\begin{matrix}{R_{T} = \frac{R_{s}}{D}} & (5)\end{matrix}$

In other words, the specific grain boundary resistivity has a reverserelation with the grain size. Since there is no direct evidence showingany physical and/or chemical changes in the grain boundary, it isexpected that as grains start to grow into the microsize range and asthe total grain boundary area decreases, the impurity concentration inthe grain boundary will increase. Normally, the presence of impuritiesin the grain boundary increase the resistivity of the grain boundary, sothe grain boundary response starts to become increasingly relevant asthe grain size increases.

Likewise, when the effects of the grain boundary response starts tobecome significant, the high frequency semi-circle representing thegrain response shrinks dramatically, suggesting that at a relativelyhigh sintering temperature the impurities originally inside of thegrains began to diffuse outside to the grain boundaries. As the grainboundary becomes the most resistive part in Sample T1200A, most of theelectric field is confined to the grain boundary instead of the grain.Since the grain boundary is relatively thin as compared to thedimensions of the grain itself (typically less than about 1 nm ascompared to a typically grain diameter of about 200 nm), the confinementof the electric field at the grain boundary gives rise to earlierbreakdown and initiates the ultimate electric breakdown process. Thisnotion is supported by I-V the curve of Sample T1200A, exhibiting thehighest leakage current and non-linear behavior.

As noted above, the grain boundary is quite thin, with a typicalthickness of less than 1 nm. The grains themselves are also unusuallysmall (typically around 200 nm in diameter), thus the total surface areaof the grains is unusually large. The grain boundary material is thusspread quite thinly over the grains, with a calculated volume of lessthan about 1.5% of the total volume of the sintered substrate. In suchsintered nanoscale substrates having substantially elevated total grainsurface area, the grain boundary phase must either be spreadsubstantially thin or present in greater than usual proportion. If thelatter, then the total amount of impurities present in the grainboundary phase would necessarily be diluted, resulting in a grainboundary phase having a substantially low concentration of impurities.Likewise, the oxygen stoichiometry and defect chemistry present in thegrain boundary phase (as well as the grains themselves) may moreprominently influence the electronic properties of the system as grainsize and grain boundary thickness decrease.

FIG. 13 plots the D.C. dielectric breakdown strength of each sinteredsample. The BDS was measured on samples with dimpled configuration (asshown in FIG. 2), and, as a result, the maximum electric stress islocated at the bottom of the dimple (i.e., the thinnest point).Consequently, the intrinsic BDS of a sintered sample was measured, asthe edge effect (field concentration at electrode edge) was thusminimized or substantially eliminated.

In FIG. 13, a reverse relationship between the BDS and the leakagecurrent was observed, which indicates that the breakdown process iselectronic in nature. Except for Sample T1200A, all the samplesexhibited breakdown strengths higher than 1000 KV/cm. This behaviorsuggests that breakdown strength might have a grain size dependence,which is in agreement with previous researches on BaTiO₃ ceramics aswell as TiO₂ ceramics. It has long been noticed that there is acorrelation between breakdown strength and mechanical strength. Sincerefinement of the grain size reduces the critical flaw size whichdetermines both mechanical strength and breakdown strength, fine gainedsamples are expected to have higher breakdown strength. However, in thiscase, sample T750 has the finest average grain size but does not exhibitthe greatest breakdown strength; this observation may be due to sampleT750's residual porosity. And for samples T900A, T900F, and T9001C, allof which were sintered at the same temperature with similar grain sizeand porosity, their differences in breakdown strength may more likely beexplained by their electrical microstructures. Under optimized sinteringconditions (FIG. 2 profile 1), the defects concentration was minimizedand the leakage current was likewise reduced. Consequently, the mostresistant sample also has the highest breakdown strength. AlthoughSample T1200A achieved almost 100% density, its breakdown strength isthe lowest observed because its overall electrical resistance is thelowest. In addition, for Sample T1200A, voltage is mainly held by thinlayer of the gain boundaries, so when critical filed stress is reachedthe grain boundary will start to fail, initiating the breakdown process.This postulate is supported by the phenomenon that during the breakdownstrength test, almost no leakage current was detected for lowtemperature sintered samples until they failed, while for Sample T1200Aa sharp increase of leakage current was observed before dielectricbreakdown occurred (as shown in FIG. 14).

According to equation (2), the highest potential energy density about 15J/cm³ is achieved on sample T9001C, which is almost an entire order ofmagnitude higher than current paper based high energy densitycapacitors.

While the novel technology has been illustrated and described in detailin the drawings and foregoing description, the same is to be consideredas illustrative and not restrictive in character. It is understood thatthe embodiments have been shown and described in the foregoingspecification in satisfaction of the best mode and enablementrequirements. It is understood that one of ordinary skill in the artcould readily make a nigh-infinite number of insubstantial changes andmodifications to the above-described embodiments and that it would beimpractical to attempt to describe all such embodiment variations in thepresent specification. Accordingly, it is understood that all changesand modifications that come within the spirit of the novel technologyare desired to be protected.

1-20. (canceled)
 21. A high energy density multilayer ceramic capacitor,comprising: at least two electrode layers; and at least onesubstantially dense polycrystalline dielectric layer positioned betweenrespective at least two electrode layers; wherein the at least onesubstantially dense polycrystalline dielectric layer has an averagegrain size of less than about 1 micrometers; wherein the at least onesubstantially dense polycrystalline dielectric layer has maximumparticle size of less than about 3 micrometers; and wherein the at leastone substantially dense polycrystalline dielectric layer has a maximumporosity of about 1 percent.
 22. The high density multilayer ceramiccapacitor of claim 21 wherein the precursor dielectric layer is selectedfrom the group including TiO₂, BaTiO₃, Al₂O₃, ZrO₂, lead zirconiumtitanate, and combinations thereof.
 23. The high density multilayerceramic capacitor of claim 21 wherein the at least one substantiallydense polycrystalline dielectric layer has a maximum porosity of about0.1 percent.
 24. The high density multilayer ceramic capacitor of claim21 wherein the at least one substantially dense polycrystallinedielectric layer has an average grain size of less than about 300nanometers.
 25. The high density multilayer ceramic capacitor of claim21 wherein the at least one substantially dense polycrystallinedielectric layer has a particle size distribution of between about 150nanometers and about 3 micrometers.
 26. The high density multilayerceramic capacitor of claim 21 wherein the at least one substantiallydense polycrystalline dielectric layer has a breakdown strength of atleast about 1100 kV per centimeter.
 27. The high density multilayerceramic capacitor of claim 21 wherein the at least one substantiallydense polycrystalline dielectric layer has a breakdown strength of atleast about 1300 kV per centimeter.
 28. The high density multilayerceramic capacitor of claim 21 wherein the at least one substantiallydense polycrystalline dielectric layer has a breakdown strength of atleast about 1500 kV per centimeter.
 29. A multilayer ceramic capacitor,comprising: a first electrode layer; a second electrode layer spacedfrom the first electrode layer; and a substantially densepolycrystalline dielectric layer positioned between the first and secondtwo electrode layers; wherein the substantially dense polycrystallinedielectric layer has an average grain size of less than about 300nanometers; wherein the substantially dense polycrystalline dielectriclayer has a breakdown strength of at least about 1100 kV per centimeterand wherein the substantially dense polycrystalline dielectric layer hasa maximum porosity of about 0.1 percent.
 30. The high density multilayerceramic capacitor of claim 29 wherein the precursor dielectric layer isselected from the group including TiO₂, BaTiO₃, Al₂O₃, ZrO₂, leadzirconium titanate, and combinations thereof.
 31. The high densitymultilayer ceramic capacitor of claim 29 wherein the at least onesubstantially dense polycrystalline dielectric layer has a maximumporosity of about 0.01 percent.
 32. The high density multilayer ceramiccapacitor of claim 29 wherein the at least one substantially densepolycrystalline dielectric layer has a particle size distribution ofbetween about 150 nanometers and about 3 micrometers.
 33. The highdensity multilayer ceramic capacitor of claim 29 wherein the at leastone substantially dense polycrystalline dielectric layer has a breakdownstrength of at least about 1300 kV per centimeter.
 34. The high densitymultilayer ceramic capacitor of claim 29 wherein the at least onesubstantially dense polycrystalline dielectric layer has a breakdownstrength of at least about 1500 kV per centimeter.
 35. A multilayerceramic capacitor, comprising: a first electrode portion; a secondelectrode portion disposed generally parallel with the first electrodeportion and spaced from the first electrode portion; and a substantiallydense polycrystalline dielectric portion positioned between the firstand second two electrode portions; wherein the substantially densepolycrystalline dielectric portion has an average grain size of lessthan about 100 nanometers; wherein the substantially densepolycrystalline dielectric portion has a breakdown strength of at leastabout 1500 kV per centimeter and wherein the substantially densepolycrystalline dielectric portion has a maximum porosity of about 0.01percent.